{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,20]],"date-time":"2025-11-20T18:35:45Z","timestamp":1763663745098},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2018,5,26]],"date-time":"2018-05-26T00:00:00Z","timestamp":1527292800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2018,12]]},"DOI":"10.1007\/s10898-018-0665-7","type":"journal-article","created":{"date-parts":[[2018,5,26]],"date-time":"2018-05-26T02:16:13Z","timestamp":1527300973000},"page":"655-678","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Generalized Lagrangian duality for nonconvex polynomial programs with polynomial multipliers"],"prefix":"10.1007","volume":"72","author":[{"given":"T. D.","family":"Chuong","sequence":"first","affiliation":[]},{"given":"V.","family":"Jeyakumar","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,5,26]]},"reference":[{"issue":"2","key":"665_CR1","doi-asserted-by":"publisher","first-page":"811","DOI":"10.1137\/110856010","volume":"23","author":"AA Ahmadi","year":"2013","unstructured":"Ahmadi, A.A., Parrilo, P.A.: A complete characterization of the gap between convexity and SOS-convexity. SIAM J. Optim. 23(2), 811\u2013833 (2013)","journal-title":"SIAM J. Optim."},{"key":"665_CR2","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718829","volume-title":"Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications","author":"A Ben-Tal","year":"2001","unstructured":"Ben-Tal, A., Nemirovski, A.: Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications. SIAM, Philadelphia (2001)"},{"key":"665_CR3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511804441","volume-title":"Convex Optimization","author":"S Boyd","year":"2004","unstructured":"Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)"},{"key":"665_CR4","doi-asserted-by":"publisher","first-page":"220","DOI":"10.1016\/j.orl.2017.03.003","volume":"45","author":"TD Chuong","year":"2017","unstructured":"Chuong, T.D., Jeyakumar, V.: Convergent conic linear programming relaxations for cone-convex polynomial programs. Oper. Res. Lett. 45, 220\u2013226 (2017)","journal-title":"Oper. Res. Lett."},{"issue":"2","key":"665_CR5","first-page":"257","volume":"1","author":"F Flores-Bazan","year":"2016","unstructured":"Flores-Bazan, F., Opazo, F.: Characterizing the convexity of joint-range for a pair of inhomogeneous quadratic functions and strong duality. Minimax Theory Appl. 1(2), 257\u2013290 (2016)","journal-title":"Minimax Theory Appl."},{"key":"665_CR6","volume-title":"Nonlinear Programming","author":"DP Bertsekas","year":"2004","unstructured":"Bertsekas, D.P.: Nonlinear Programming, 2nd edn. Athena Scientific, Nashua (2004)","edition":"2"},{"key":"665_CR7","unstructured":"Grant, M., Boyd, S.: CVX: Matlab software for disciplined convex programming, version 2.1, Mar 2014. http:\/\/cvxr.com\/cvx"},{"issue":"1","key":"665_CR8","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1007\/s10107-008-0240-y","volume":"122","author":"JW Helton","year":"2010","unstructured":"Helton, J.W., Nie, J.: Semidefinite representation of convex sets. Math. Program. Ser. A 122(1), 21\u201364 (2010)","journal-title":"Math. Program. Ser. A"},{"key":"665_CR9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02796-7","volume-title":"Convex Analysis and Minimization Algorithms. I. Fundamentals","author":"J-B Hiriart-Urruty","year":"1993","unstructured":"Hiriart-Urruty, J.-B., Lemarechal, C.: Convex Analysis and Minimization Algorithms. I. Fundamentals. Springer, Berlin (1993)"},{"key":"665_CR10","doi-asserted-by":"publisher","first-page":"707","DOI":"10.1007\/s10957-014-0545-3","volume":"163","author":"V Jeyakumar","year":"2014","unstructured":"Jeyakumar, V., Lasserre, J.-B., Li, G.: On polynomial optimization over non-compact semi-algebraic sets. J. Optim. Theory Appl. 163, 707\u2013718 (2014)","journal-title":"J. Optim. Theory Appl."},{"issue":"1\u20132","key":"665_CR11","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1007\/s10107-013-0716-2","volume":"147","author":"V Jeyakumar","year":"2014","unstructured":"Jeyakumar, V., Li, G.: Trust-region problems with linear inequality constraints: exact SDP relaxation, global optimality and robust optimization. Math. Program. Ser. A 147(1\u20132), 171\u2013206 (2014)","journal-title":"Math. Program. Ser. A"},{"issue":"3","key":"665_CR12","doi-asserted-by":"publisher","first-page":"735","DOI":"10.1007\/s10957-013-0496-0","volume":"162","author":"V Jeyakumar","year":"2014","unstructured":"Jeyakumar, V., Vicente-Perez, J.: Dual semidefinite programs without duality gaps for a class of convex minimax programs. J. Optim. Theory Appl. 162(3), 735\u2013753 (2014)","journal-title":"J. Optim. Theory Appl."},{"key":"665_CR13","doi-asserted-by":"publisher","DOI":"10.1142\/p665","volume-title":"Moments, Positive Polynomials and Their Applications","author":"JB Lasserre","year":"2009","unstructured":"Lasserre, J.B.: Moments, Positive Polynomials and Their Applications. Imperial College Press, London (2009)"},{"key":"665_CR14","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107447226","volume-title":"An Introduction to Polynomial and Semi-algebraic Optimization, Cambridge Texts in Applied Mathematics","author":"JB Lasserre","year":"2015","unstructured":"Lasserre, J.B.: An Introduction to Polynomial and Semi-algebraic Optimization, Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge (2015)"},{"issue":"10","key":"665_CR15","doi-asserted-by":"publisher","first-page":"1474","DOI":"10.1109\/9.256366","volume":"73","author":"DG Luenberger","year":"1992","unstructured":"Luenberger, D.G.: A double look at duality. IEEE Trans. Autom. Control 73(10), 1474\u20131482 (1992)","journal-title":"IEEE Trans. Autom. Control"},{"key":"665_CR16","doi-asserted-by":"crossref","unstructured":"Mordukhovich, B.S., Nam, N.M.: An easy path to convex analysis and applications. Synthesis Lectures on Mathematics and Statistics, vol. 14. Morgan & Claypool Publishers, Williston (2014)","DOI":"10.1007\/978-3-031-02406-1"},{"issue":"1\u20132","key":"665_CR17","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1007\/s10107-013-0680-x","volume":"146","author":"J Nie","year":"2014","unstructured":"Nie, J.: Optimality conditions and finite convergence of Lasserre\u2019s hierarchy. Math. Program. Ser. A 146(1\u20132), 97\u2013121 (2014)","journal-title":"Math. Program. Ser. A"},{"key":"665_CR18","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1512\/iumj.1993.42.42045","volume":"42","author":"M Putinar","year":"1993","unstructured":"Putinar, M.: Positive polynomials on compact semi-algebraic sets. Indiana Univ. Math. J. 42, 203\u2013206 (1993)","journal-title":"Indiana Univ. Math. J."},{"key":"665_CR19","doi-asserted-by":"publisher","DOI":"10.1515\/9781400873173","volume-title":"Convex Analysis","author":"RT Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)"},{"key":"665_CR20","unstructured":"Toh, K.C., Todd, M.J., Tutuncu, R.H.: SDPT3\u2014a MATLAB software for semidefinite\u2013quadratic\u2013linear programming. http:\/\/www.math.nus.edu.sg\/~mattohkc\/sdpt3.html"},{"issue":"3","key":"665_CR21","doi-asserted-by":"publisher","first-page":"1045","DOI":"10.1007\/s10898-012-9917-0","volume":"56","author":"H Tuy","year":"2013","unstructured":"Tuy, H., Tuan, H.D.: Generalized S-lemma and strong duality in nonconvex quadratic programming. J. Glob. Optim. 56(3), 1045\u20131072 (2013)","journal-title":"J. Glob. Optim."}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-018-0665-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-018-0665-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-018-0665-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,2]],"date-time":"2023-09-02T20:45:37Z","timestamp":1693687537000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-018-0665-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,26]]},"references-count":21,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2018,12]]}},"alternative-id":["665"],"URL":"https:\/\/doi.org\/10.1007\/s10898-018-0665-7","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,5,26]]},"assertion":[{"value":"31 May 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 May 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 May 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}